Hamiltonian Assignment for Open Quantum Systems

TL;DR

This paper develops methods to identify Hamiltonians of open quantum systems using a polynomial number of measurements, validated through simulations of spin chains, and explores robustness against noise.

Contribution

It introduces novel Hamiltonian estimation techniques for open quantum systems based on stationary and dynamical equations, with validation on spin chain models.

Findings

Estimator accuracy improves with relaxed physicality constraints in some cases

Methods are effective with polynomial measurement complexity

Simulation results confirm robustness against systematic noise

Abstract

We investigate the problem of determining the Hamiltonian of a locally interacting open-quantum system. To do so, we construct model estimators based on inverting a set of stationary, or dynamical, Heisenberg-Langevin equations of motion which rely on a polynomial number of measurements and parameters. We validate our Hamiltonian assignment methods by numerically simulating one-dimensional XX-interacting spin chains coupled to thermal reservoirs. We study Hamiltonian learning in the presence of systematic noise and find that, in certain time dependent cases, the Hamiltonian estimator accuracy increases when relaxing the environment's physicality constraints.